When generating the resident yubikey SSH key, is the secret key generated on the computer really safe?

According to https://stephentanner.com/ssh-yubikey.html to generate a key on my yubikey I should do:

ssh-keygen -t ed25519-sk -O resident -O verify-required -C "Main Key"

I did and touched the yubikey and used an empty password and it generated the _sk file. The blog says it should be a pointer to the actual key inside the yubikey but when I print it, it looks exactly like a secret key:

-----BEGIN OPENSSH PRIVATE KEY-----
... bunch of data

should it indeed be like this?

Do I need to copy this and use on all computers where I want to use the yubikey key? Shouldn’t it defeat the purpose of having the key entirely on the yubikey?